Virginia Commonwealth University was awarded a three-year $202,121 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049).
The grant will fund research into nonlocal variational problems arising from physical and biological models. VCU researchers will develop new mathematical tools to analyze symmetry properties of optimizers for a model describing oppositely charged phases. They will also study how regularization via interfacial free energy affects swarming models with attractive-repulsive nonlocal energies. A third aim is to extend Gamow's liquid drop model to investigate the effect of neutrons on nuclear shape and fission thresholds. Researchers will apply techniques from nonlinear analysis, optimization, partial differential equations and computer experimentation. The grant supports the training of undergraduate and graduate students through involvement in the research projects. Overall, the funding will advance understanding of structure formation in physical systems through nonlocal variational models, with potential implications across material science, quantum mechanics, biology and other fields.